Shear flow suppression of hotspot growth
by
Matthew Finn
The University of Adelaide
Coauthors: Stephen Cox, Richard Clarke

We consider the role of fluid shear in maintaining anomalous hotspot solutions reported for a chaotically stirred bistable chemical reaction model [Cox, Phys. Rev. E 056206, 2006]. In the well-mixed regime, the chemical concentration satisfies an autonomous ordinary differential equation with two stable equilibria. The reaction proceeds to extinction or to an excited state depending on whether the initial concentration lies below or above an unstable threshold. However, if the concentration varies spatially, and the chemical is stirred, the interplay between advection, diffusion and reaction is complicated, and the fate of the reaction depends sensitively on initial conditions. Moreover, if stirring is temporally periodic, localised hotspots can emerge which never become extinct or excited. In the current work we show that shear plays a role in maintaining hotspots, and derive a simple dynamical system to predict the fate of a stripe of chemical in a shear flow.

Date received: October 20, 2009